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Erschienen in:
2020 | OriginalPaper | Buchkapitel
6. State Linear Systems
verfasst von : Ruth Curtain, Hans Zwart
Erschienen in: Introduction to Infinite-Dimensional Systems Theory
Verlag: Springer New York
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Abstract
In this chapter the system differential equation \(\dot{z}(t) = A z(t) + B u(t)\), \(y(t) = C z(t) + D u(t)\) is introduced. For this state linear system the concepts of controllability and observability are defined, and it shown that there are different generalisations of their finite-dimensional counterparts. Using the characterisation of invariant subspaces of Chaps. 2 and 3, tests for controllability and observability are derived for the different classes of systems. Since the controllability and observability gramian satisfy a Lyapunov equation, a section on Lyapunov equations is also part of this chapter. The chapter ends with a set of 28 exercises and a notes and references section.